Hardy-Sobolev Type Inequalities with Sharp Constants in Carnot-Carath,odory Spaces

被引：26

作者：

Danielli, Donatella ^{[1
]}

Garofalo, Nicola ^{[1
]}

Phuc, Nguyen Cong ^{[2
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

来源：

POTENTIAL ANALYSIS | 2011年 / 34卷 / 03期

基金：

美国国家科学基金会;

关键词：

Hardy type inequalities; Carnot groups; Carnot-Carathcodory spaces; Horizontal p-Laplacian; CARNOT-CARATHEODORY SPACES; HEISENBERG-GROUP; VECTOR-FIELDS; SUBELLIPTIC EQUATIONS; FUNDAMENTAL-SOLUTIONS; UNIQUE CONTINUATION; HEAT-EQUATION; OPERATORS; THEOREMS; SURFACE;

D O I：

10.1007/s11118-010-9190-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a generalization with sharp constants of a classical inequality due to Hardy to Carnot groups of arbitrary step, or more general Carnot-Carath,odory spaces associated with a system of vector fields of Hormander type. Under a suitable additional assumption (see Eq. 1.6 below) we are able to extend such result to the nonlinear case p not equal 2. We also obtain a sharp inequality of Hardy-Sobolev type.

引用

页码：223 / 242

页数：20

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